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The derivative of the function/ 4sinx-5x^8

Derivative of 4sinx-5x^8

The solution

You have entered [src]

              8
4*sin(x) - 5*x

$$- 5 x^{8} + 4 \sin{\left(x \right)}$$

4*sin(x) - 5*x^8

Detail solution

Differentiate $- 5 x^{8} + 4 \sin{\left(x \right)}$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of sine is cosine:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  So, the result is: $4 \cos{\left(x \right)}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{8}$ goes to $8 x^{7}$
  So, the result is: $- 40 x^{7}$
The result is: $- 40 x^{7} + 4 \cos{\left(x \right)}$

The answer is:

$- 40 x^{7} + 4 \cos{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      7           
- 40*x  + 4*cos(x)

$$- 40 x^{7} + 4 \cos{\left(x \right)}$$

Simplify

The second derivative [src]

   /    6         \
-4*\70*x  + sin(x)/

$$- 4 \left(70 x^{6} + \sin{\left(x \right)}\right)$$

Simplify

The third derivative [src]

   /     5         \
-4*\420*x  + cos(x)/

$$- 4 \left(420 x^{5} + \cos{\left(x \right)}\right)$$

Simplify